In terms of the coherent states used to construct the functional
integral (REF ), the components of the number index
\({\rm n}\)  correspond to a bilinear form \(n_p = {\xi }^{\dagger }_p {\xi }_p\) .
The number field may be made an elementary degree of freedom as part
of a canonical transformation [1]} of the
coordinates of the Hamiltonian dynamical system,
\({\xi }_p^{\dagger }& \equiv e^{{\eta }_p}&{\xi }_p& \equiv e^{-{\eta }_p}n_p .\) 
